Sensor for optically sensing air borne acoustic waves

ABSTRACT

The present invention relates to an optical sensor of air borne acoustic waves. The sensor comprises means for producing mutually coherent optical sampling and reference beams, which may be combined to form an intermediate frequency carrier, the sampling beam being exposed to the acoustic field, in which acoustic wave induced density variations occur. These density variations produce a variation in the index of refraction and thereupon a phase modulation of the sampling beam. This phase modulation may be recovered by an optical detector and a phase detector as an electrical signal representative of the acoustic signal. 
     The invention has application to security systems.

RELATED APPLICATION

The present invention is related to the application of Monsay, Penn, andWinfield, assigned to the Assignee of the present application, andentitled “Sensor And An Array of Sensors For Optically Sensing WaterBorne Acoustic Waves” (35-HE-1514), Ser. No. 864,260 filed concurrentlyherewith on May 19, 1987.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a novel acoustic wave sensor forsensing acoustic waves in a fluid typically air. The invention employsoptical techniques, and more particularly depends upon the phasemodulation which occurs when coherent light is passed through a fluid inwhich acoustic waves occur. The phase modulation may be imposed on acarrier provided by optical heterodyning and then detected electrically.The electrical signal recovered in this manner is representative of theacoustic waves.

2. Description of the Prior Art

In the patent application of Gordon Jacobs, Ser. No. 507,528 filed Sep.19, 1974 entitled “Laser Hydrophone and Virtual Array of LaserHydrophones”, an acoustic sensor employing optical techniques wasearlier proposed. The sensor, which was termed a “hydrophone”, since itwas designed for use in water, employed a laser beam which was focusedon a small “focal” volume of water in which natural light scatteringmatter was suspended. The scattering matter, which vibrates insynchronism with any acoustic waves present, produces a phase modulationof the scattered light. The phase modulation was then recovered byoptical heterodyne and sensitive phase demodulation techniques. TheJacobs arrangement contemplated both single hydrophones and arrays ofhydrophones. In general, optical arrays, such as the Jacobs arrays,produce less hydrodynamic disturbance than the known large areapiezoelectric arrays.

The Jacob's arrangement was dependent upon a “doppler” type shift infrequency or phase, the doppler shift being caused by particle motion,toward and away from the sensing beam. Thus the maximum sensitivity wasobtained by pointing the laser beam in a direction toward the source ofacoustic waves and perpendicular to the wave fronts.

The present invention shares certain of the objectives and in usingoptical techniques, certain of the means of the foregoing Jacobs'invention.

The Jacobs invention is unlike the present invention which hasapplication to the detection of acoustic waves in the air. The presentinvention has application to security systems, as for instance in themonitoring of sounds occurring along the perimeter of a property.

SUMMARY OF THE INVENTION

Accordingly it is an object of the present invention to provide animproved sensor of acoustic waves occurring in a fluid medium.

It is another object of the present invention to provide an improvedoptical acoustic sensor for sensing air borne acoustic waves.

These and other objects of the invention are achieved in an opticalacoustic sensor comprising means for producing mutually coherent opticalsampling and reference beams; optical means including an aperture atwhich the path of the sampling beam into the air is initiated and afterreflection is terminated, and light reflective means arranged in thepath of the sampling beam for reflecting significant sampling beamenergy back via the aperture.

The optical acoustic sensor further comprises an optical detector forcoherently combining the reflected sampling beam with the reference beamto form an electrical heterodyne signal, phase modulated as result ofthe acoustic wave induced variation in the index of refraction, andfinally a phase detector coupled to the output of the optical detectorfor detecting the acoustic wave induced phase variation of the samplingbeam and thereby recovering an electrical signal representative of theacoustic waves.

In accordance with the invention, the initial and reflected portions ofthe sampling beam path between aperture and the light reflective meansare oriented with a substantial component parallel to the acousticwavefronts of the acoustic waves. For maximum sensitivity, the samplingbeam path is parallel in the farfield or tangential in the nearfield tothe acoustic wave fronts. With a substantial component parallel to theacoustic wave front, the sampling beam is exposed to an acoustic waveinduced density variation of like amplitude over a portion of the pathof the sampling beam. As the acoustic waves traverse the path of thebeam of light, the density variation produced by the acoustic wave,causes the index of refraction of the fluid (air) to vary, and thereuponphase modulates.the sampling beam. The amount of phase modulation is inproportion to the accumulated variation in the index of refraction overthe beam path.

BRIEF DESCRIPTION OF THE DRAWINGS

The inventive and distinctive features of the invention are set forth inthe claims of the present application. The invention itself howevertogether with further objects and advantages thereof may best beunderstood by reference to the following description and the followingdrawings in which

FIG. 1 is an illustration, partially in block diagram format andpartially in perspective, of a single optical acoustic sensor foroptically sensing air borne acoustic waves;

FIG. 2 is a perspective view of an optical acoustic sensor mounted upona vehicle, for optically sensing air borne acoustic waves, as forinstance conversations, the sensor using a non-specular opticalreflector; and

FIG. 3 is a perspective view of an arrangement employing a plurality ofoptical acoustic sensors mounted along consecutive line segments of aproperty line with optical transmitter/receivers and retro-reflectors atopposite segment ends, the arrangement being designed to optically senseair borne acoustic waves from near sources along the perimeter of aproperty for intrusion monitoring.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

An optical acoustic sensor for optically sensing fluid borne acousticwaves is illustrated in FIG. 1. The sensor has as its principal optical,or light handling, components, the elements 10 to 23, and as itsprincipal electrical or electrical signal handling components, theelements 24 to 27. The fluid, for instance air, in which the acousticwaves to be optically detected occur, is portrayed in the righthandportion of FIG. 1, with the acoustic wavefronts bearing the referencenumeral 28. The source of acoustic wavefronts is not shown, being beyondthe area of the illustration. (As will be explained, the featuresdepicted in the righthand position of FIG. 1 are shown with substantialdistortion in scale.)

The optical elements produce a coherent optical beam which is projectedinto the fluid in which the acoustic waves occur, and recover areflected optical beam which is phase modulated by its exposure to theacoustic waves. The process entails formation of an optical heterodynein which a sampling “beam” is projected into the fluid and recovered byreflection, while a reference beam at an offset frequency is prepared toform an optical heterodyne with the returning sampling beam. Theacoustic wave induced optical phase modulation is recoverable from thisheterodyne. The optical heterodyne frequency is set for convenientrecovery in an electrical format of the phase modulation at thephotodetector 23. The heterodyne frequency may not exceed the bandwidthof the photodetector. The electrical components, which operate upon themodulated optical signal after conversion to an electrical format,prepare the signal for display, aural reproduction, or otherutilization.

The optical elements of the optical acoustic sensor, which enter intothe formation and recovery of the sampling beam, include the laser 10, afirst beamsplitter 11, a first (plus) 40.1 Mhz Bragg modulator 12, withan accompanying 40.1 Mhz driver 13, and optical means including anapertured barrier 14 and an optional collimating lens 15 at theinterface with the air in which the acoustic waves occur. A remotereflector 16 is provided at a fixed distance from the optical means 14.The optical means 14, 15, also in the return path of the sampling beam,is followed by the beam splitter 17, and the photodetector 23, which isthe last optical element of the system.

The optical elements which enter into the formation of the referencebeam include the beam splitter 11, at which the reference beam isseparated from the sampling beam at the output of the laser 10, a secondplus (40 Mhz) Bragg modulator 18, with an accompanying 40 Mhz driver 19,a mirror 20, an optical delay 21 equal to the delay encountered in thesampling process, a pair of additional mirrors 22 for beam alignmentpurposes, a beam splitter 17 used for combining the reference beam withthe returning sampling beam, (the actual optical heterodyne appearing atthe surface of the photo-detector 23), and the photodetector 23 the lastoptical element of the optical system, as noted above. The opticalheterodyne, appearing at the photodetector 23, is an electrical signalphase modulated by the acoustic wave.

The electrical processing elements following the photodetector 23consist of an amplifier 24, a narrow band filter 25 (100 Khz+30 Khz), aphase detector for recovering phase and amplitude information from theacoustic wave, and a processor 27 in which further processing occursprior to the final presentation of the information in a display orreproducer.

As previously noted, the acoustic waves of interest are illustrated inthe right hand portion of FIG. 1 in which the air environment isdepicted between the apertured partition and the collimator (14, 15) onthe one hand, and the mirror 16 on the other hand. In the figure, thesampling beam (29, 30) proceeds to the right in a horizontal plane, (theillustration being a plan view looking toward the ground from a positionabove the ground) the sampling beam continues until it impinges on thereflector 16 and then returns on a slightly displaced but stillhorizontal path to the collimator 15. (The outgoing portion of thesampling beam bears the reference numeral 29 and the reflected beam thereference numeral 30.)

The acoustic waves in the illustration are intended to represent wavesoriginating from a source beyond the bottom limits of the illustration.The source of the waves is assumed to be in a horizontal plane, and thedistance is sufficiently small that the wavefronts 28 have curvature.The wavefronts are also assumed to be tangential to the path of thelaser beam implying that the azimuthal position of the remote source isorthogonal to the sampling beam path. The acoustic frequencies mayextend over a range in excess of 300 to 1; i.e., from below 50 to above15,000 Hz. Assuming that the speed of sound in air is 330 meters persecond, the spacing between wavefronts varies from two centimeters orless at the highest frequencies to 6.6 meters or more at the lowerfrequencies. A reasonable figure for the path length of the opticalsampling beam between the aperture and the reflector is from 10 to 200meters, but depending upon application, may be much larger.

The scale distortion in FIG. 1 requires some discussion. The relativescale as between the distance between maxima of the acoustic waves 28and the sampling path length from 14, 15 to 16 may accordingly beundistorted at one wavelength within the 300 fold frequency range anddistorted at all other wavelengths. The lens aperture dimension and theseparation between outgoing and incoming sampling beams are both drawnsubstantially larger than to scale, for instance in relation to thesampling path length. In continuous wave (cw) of transmission, the beams29 and 30 should be mutually displaced at the lens 15 to facilitatetheir separation, but not in the amount suggested by the scale. Eachbeam is typically 1-5 millimeters in cross-section, and the lens 15 maybe 10 to 15 millimeters in diameter. The greatest separation of the twosampling beam paths would thus be in about 10 millimeters. The beamseparation is so extremely small in the scale of the drawing, as to benot readily depicted. (Assuming 1 meter equals one inch for depictingacoustic wavelengths, 10 millimeters would equal {fraction (1/100)} ofan inch.) Thus from the practical point of view of sensing an acousticwave at the same phase position, the wavefronts of the wave being 2meters apart, the paths 29 and 30, which are separated at most by 10millimeters and representing a phase error in the sonic wave of only twodegrees, are practically co-incident. Even though displaced, the twoparts of the sampling beam may properly be represented by a singlenarrow line, not treated as introducing any significant error into thephase detection process.

In the optical acoustic sensor so far described with relation to FIG. 1,continuous wave (cw) laser operation is intended, and this isfacilitated by displacing the outgoing from the incoming beams on thesurface of the lens 15 so as to permit separation of the light in theprocessor. In the processor, the optical output of the Bragg modulation12 goes through one portion of the lens 15 and the return beam entersthrough another portion of the lens 15 where it is intercepted by thebeam splitter 17. The displacement of the beams permits the acousticsensor to form the heterodyne continuously, without being pulsed.

One may however employ an arrangement in which the outgoing and incomingsampling waves follow an overlapping path as they enter and returnthrough the lens 15. In the case where the beam paths overlap, theincoming waves should return to the beam splitter at a time that theoutgoing wave transmission is suspended. Pulsing would achieve this end.The pulse interval should be selected to avoid simultaneous transmissionand reception at the optical path length of the optical sensor.

The optimum orientation of the beam path to the acoustic wavefront formaximum sensitivity is the tangential relationship illustrated in FIG.1. It is assumed that the object is sufficiently close that thewavefronts 28 are curved, although tangential at some point along thesampling beam. Thus the sampling beam, which travels in a linear pathacross the curved acoustic wavefront, will be exposed at a substantialportion of the beam path to a acoustic wave in the same condition ofcompression or rarifaction. The result of exposure to the condition of amaximum compression is the production of a maximum integrated index ofrefraction, which results in a maximum amount of phase shift of thelight beam. Similarly at some time earlier or later, the sampling beamwill be similarly exposed to a fluid under the same minimum compression.Exposure to this condition produces a minimum integrated index ofrefraction, which results in a minimum amount of phase shift of thelight beam.

The optimum orientation of the beam path for maximum sensitivity to anear field source of acoustic waves is with beam path and wavefrontstangential. In principle, greater absolute sensitivity may exist in afarfield relationship in which the wavefronts are straight lines,impinging exactly parallel to the beam path. The effect of curvature ofthe wavefront results in a loss in sensitivity in that only a shortsegment of the beam path, wavelength dependent, and in the first Fresnelzone, is effective and uncancelled. This loss in absolute sensitivity isless than the increase in power density as the source approaches thebeam path, and thus the detected signal level will increase as thereciprocal of the first power of the distance. In addition, the soundsource need not be in the optimum azimuthal position orthogonal to thebeam path at the center of the beam path. Sensitivity falls off onlywhen the point of orthogonality between the optical beam and theacoustic beam comes close to the end of the optical beam. After this,the sensitivity falls off as the acoustic source is no longer orthogonalanywhere to the sampling beam path, and then the fall-off is gradual andwavelength dependent. As will be shown, the photon-noise-limitedsensitivity is very good, so that if there is a reasonable (uncancelled)component of the acoustic wavefront in the sampling beam path, asubstantial signal may usually be obtained.

As will be better appreciated as the further embodiments of theinvention are discussed, the beam path may be relatively long, givingrise to the possibility that there will be a plurality of positionsalong the beam path at which sound sources will occur. The sources willoften be in the “near field” pattern and their wavefronts will exhibitappreciable curvature as they intersect the beam path. The wavefrontswill however, be tangential to the beam at one point along the beampath, creating a first Fresnel zone sensitivity.

However, as the wavelength decreases, the Fresnel zone narrows, and thesensitivity decreases. Thus the higher frequency acoustic waves, inreducing the effective length of the beam path (i.e. the first Fresnelzone) will be attenuated more than the longer wave lengths at a givenproximity of the source to the beam path (disregarding the effect ofbandwidth in the electronic signal processing).

The optical acoustic sensor so far described is operable as a singleunit for sensing air borne acoustic waves. In summary, the sensor may beseen to include the laser 10, the beam splitter 11, and the first 40.1Mhz Bragg modulator 12 and its associated driver 13 for producing acoherent optical sampling beam. At the same time, the same laser 10 andsame beam splitter 11, a second 40 Mhz Bragg modulator 18 and associateddriver and remaining optical elements 20, 21, 22 and 17 produce amonochromatic optical reference beam, mutually coherent with thesampling beam, and assist in superimposing the reference beam upon thesampling beam at the optical detector 23.

The apertured wall 14 and collimating lens 15 constitute the opticalmeans for initiating the path of the sampling beam into the air in whichthe acoustic waves are present and for terminating the path by which thereflected beam returns. The collimating lens 15 also maintains thesampling beam, while the acoustic field, at a cross-sectional dimensionwhich is small in relation to the acoustic waves of interest. In theFIG. 1 embodiment, the collimating lens is a small lens set in anaperture of a wall.

The reflector 16 is arranged in the air in the acoustic field. It isarranged in the path of the sampling beam at a fixed distance from thelens aperture combination with an orientation set to reflect thesampling beam back almost upon itself, to the lens aperture. Forefficiency, the reflector 16 may be a specular mirror, and in practice,if specular, it must be a retro-reflector, which can return thereflected beam to a position which must be exact to less than the beamwidth for super position with the reference beam. This accuracy isrequired since the reference and sampling beams must be superimposed atthe photo-detector. If the distances are small and the available poweradequate, a non-specular reflective surface which reflects some fractionof the beam back for imaging on the photodetector surface may also beemployed.

The phase modulation is recovered by the optical detector 23 at whichthe sampling and reference beams are coherently combined to form thephase modulated electrical heterodyne signal. Here the basic doubleheterodyne approach of using a plus 40.1 and a plus 40 Mhz Braggmodulator produces a 100 Khz carrier at the photodetector output. Theacoustic wave induced phase modulation of the light beam appears as amodulation upon this carrier.

The double heterodyne approach may involve either a single Braggmodulator in each of the sampling and reference beam paths as shown, ortwo Bragg modulators in one path. One need not, however, employ thedouble heterodyne approach since in many types of electrical detectioncircuits, a larger intermediate frequency is quite usable.

The optical acoustic sensor, which includes the amplifier 24 and filter25 following the photodetector, is completed by a phase detector 26coupled to the output of the optical detector. The phase detector 26produces an electrical signal which is responsive to and replicates theacoustic waves in the acoustic field. The electrical signal, whilerelatively low in frequency since it corresponds to the frequencies ofthe acoustic waves, may be seen to contain both the instantaneousamplitude of the wave and as the amplitude is being received as afunction of time, the phase of the wave. Thus the optical acousticsensor element is adaptable for use as an element of an array of likedevices, should one desire greater sensitivity and greater accuracy indetermining the azimuthal position of a remote source of sound.

FIG. 2 is a perspective view of an optical acoustic sensor mounted upona vehicle for optically sensing remote air borne acoustic waves, as forinstance conversations, the sensor utilizing a non-specular opticalreflector to return the laser beam back to the sensor.

Referring now to FIG. 2, the laser transmitter/receiver is housed in anenclosure 41 on the roof of the van seen in the foreground of thepicture. Conversations are presumably taking place between the twostanding individuals shown in the foreground and the acoustic waves 42produced by the conversation are propagating across the picture to theright where they intersect the path of a laser beam shown at 43. Thelaser beam 43, which is initiated at the housing 41, continues throughthe open air to the right of the standing individuals, and is exposedthere to the sonic waves 42 propagating across the path of the laserbeam. The laser beam continues until it impinges on the masonry base 44surrounding the fountain. The laser beam, upon impinging on the base 44,is in fact reflected in a number of directions, but the reflection ofinterest, is the backward reflection which returns a portion of the beamalong essentially the same path 43, where it is intercepted at theenclosure 41 on the roof of the van.

A similar opportunity for detecting remote conversations is illustratedin relation to the seated couple in the background of the picture and tothe right. A laser beam 45 is shown passing adjacent the seatedindividuals, where it encounters the sonic waves, depicted at 46, andthen after impingement on the wall 47, some portion of the laser beamreturns along essentially the same path that the beam followedoriginally.

Because of the non-specular nature of the reflection, the power level ofthe laser beam which is returned to the enclosure 41 is low.Accordingly, the transmitted laser power should be relatively high. Thepower level and direction of the laser beam should be selected so as toavoid injury. (The monitoring of the conversations must of course be inaccordance with the laws affecting privacy.)

FIG. 3 is a perspective view of an arrangement for optically sensing airborne acoustic waves from near sources along the boundary of a propertyfor intrusion monitoring. The arrangement entails a plurality of opticalacoustic sensors mounted along line segments of the boundary. In theillustration, the property is four sided and therefore entails the useof four optical acoustic sensors. The sensors, as in the FIG. 1embodiment, each consist of a optical transmitter/receiver, for exampleat 51 at the south-west corner of the property and a retro-reflector at52 at the northeast corner of the property. This sensor monitors theeastern line boundary segment. Similar acoustic sensors at 53-54, 55-56,57-58, each consisting of an optical transmitter/receiver and aretro-reflector are located at the respective ends of the northern,western and southern line segments to provide complete coverage aroundthe perimeter of the property.

Assuming that the distances in the FIG. 3 embodiment are moderate, forexample under 1,000 meters, the optical transmitters may employ lowpower diode lasers. The use of the specular, retro reflectors at thecorners, assuming a low degree of attenuation in the beam path and goodbeam collimation, tends to minimize the amount of power required forreasonable acoustic sensitivity. If, however, all-weather sensitivity inmist, rain, and snow is desired, this may be accomplished by increasingthe laser power, sheltering the beam path from precipitation andgenerally increasing the quality of collimation and reflection.

In the example, the use of low power diode lasers facilitates aneye-safe installation, the optical path traversed by the sampling beambeing above the heads of prospective intruders and the optical powerlevels being such that casual exposure to the beam would be unlikely toproduce eye injury.

The detection pattern, as has been suggested earlier, is one in whichwavefronts tangential to the sampling beam path provide maximumsensitivity of response in the sensor in a first Fresnel zone. Asdesigned, the sensor has no true blind spots. All sources along the linesegments will at some point create waves tangential to the beam pathproducing a useful signal. At the ends of the line segments, theacoustic waves will avoid cancellation effects, and since acoustic wavespropagate around corners, also be detectable.

The electrical signal processing is conveniently performed such as toreproduce the acoustic waves in a sonic format over a loudspeaker orheadset to a person monitoring the system. One can, of course, employalarm systems which are unattended except upon the activation of analarm. Maximum sensitivity is produced as the acoustic wavelengthlengthens since a longer portion of the beam path will be in the firstFresnel zone.

The beam cross-sections should be maintained to less than half anacoustic wave length to avoid attenuation of the acoustic signal due toaveraging in the direction of acoustic wave propagation.

In the retro-reflector variation illustrated in FIG. 3, the maximumeffective beam cross-section is set by the aperture through which boththe outgoing and returning beam must pass. For “CW” laser operation, thereturning beam must be offset from the reference beam at the aperture,but superimposed at the photo-detector. Accordingly, the practical beampath cross-section may be from two (the minimum) to three or four beamdiameters.

The beam cross-section with a specular, retro-reflector is ordinarilydictated by the size of the available source. If low power diode lasersare to be employed, the source is a few millimeters (1-5), and the beampath cross-section for CW operation usually less than 1 centimeter.Assuming an upper acoustic frequency limit of 15 Khz, the beamcross-section may be as large as 1 cm (one-half acoustic wavelength)before a 3 db loss in sensitivity at 15 Khz would occur.

If longer paths for the sampling beam are desired, a gas laser may beemployed. Here again, larger beam cross-sections may be employed with aloss in higher frequency response.

As an alternative to a CW system, one may employ a pulsed system, inwhich the retro-reflectors are adjusted to effect coincidence betweenthe outgoing sampling beam at the aperture as well as at thephoto-detector. In this case pulsing may be used to avoid interferenceat the photodetector by allowing formation of the heterodyne signal onlyupon the return of the sampling beam. In the pulsed system, theadjustment of essentially exact coincidence between the outgoing andreturning portions of the sampling beam, makes the cross-section of thebeam path essentially equal to the beam cross-section, and provides someincrease in high frequency response.

With non-specular reflection, the need for significant laser powerincreases by several orders of magnitude. Thus, diode lasers generallywill not provide sufficient optical power for such practicalapplications, and high power gas lasers or “slab” lasers will berequired.

The calculated photon-noise-limited acoustic sensitivities of thesensors herein described are very good but hard to realize in practice.The photon-noise limited minimum detectable acoustic intensity in air,(I_(a)), (nearfield) at 1 Khz bandwidth and acoustic frequency of 1 Khzat a distance from the acoustic source of 10 meters, with a receivedoptical power of 10 milliwatts, is calculated to be equal to 2.5×10⁻¹⁸watts/cm².

The photon noise limited sensitivity, which appears to represent theultimate limit of sensitivity, exists with other often largercontributions to sensor noise. Optical bench conditions in a laboratoryproduce the nearest approach to photon noise limits. In a practicalenvironment, a major contribution to sensor noise is motion of theoptical transmitter/receiver, motion of the reflector and motion of theintervening air and air borne particles in the path of the beam.Equipment motion need only be of optical wavelengths in magnitude toaffect sensor performance. Thus for increased sensitivity, a practicaldesign must generally achieve a reduction in vibrations and resonancesthrough the acoustic frequencies of interest, achieve ridgitity in thedimensions critical to sensor operation, and minimize air turbulence inthe beam path of the sensor.

Theoretical predictions lead one to expect the minimum detectableacoustic intensity I_(a) based on the quantum (photon) noise limit forthe optical acoustic sensor in the farfield region to be:$\begin{matrix}{I_{a} = \frac{h\quad c_{o}\lambda \quad B\quad \rho \quad c_{a}^{3}}{32\pi^{2}{P_{o}\left( {n - 1} \right)}^{2}L^{2}\sin \quad {c^{2}\left( \frac{\theta \quad L}{\Lambda} \right)}}} & (1)\end{matrix}$

where h is Planck's constant

c_(o) is the speed of light

λ is the optical wavelength

B is the electronic bandwidth

ρ is the density (of the air)

c_(a) is the acoustic velocity in air

P_(o) is the received optical power

η is the quantum efficiency of the photodetector

n is the index of refraction of air

L is the interaction length of the optical beam (in the farfield region,the full length)

θ is the angle between the beam path and the acoustic wavefront, and

Λ is the acoustic wavelength.

The “sinc” function$\left( {{of}\quad {the}\quad {form}{\quad \quad}\frac{\sin/X}{X}} \right)$

in the denominator of expression (1) expresses the directionality of thesensor under farfield conditions. The greatest sensitivity, occurs whenthe argument θ is equal to zero, under which condition the sinc functiongoes to one, its maximum value making I_(a) smallest. The sinc functionbecomes zero when the argument equals unity [sinc (1)=0]. Therefore theangular increment over which the sensitivity is close to the maximum is${\Delta \quad \theta}\quad = {\frac{\Lambda}{L}.}$

In other words, the angular increment in radians at strong sensitivityis the reciprocal of the number of acoustic wavelengths in the length ofthe sensor beam. Outside of this angular increment, it is expected thatthe sensitivity will be uselessly poor.

In the nearfield case, assuming the beam path is many acousticwavelengths long and therefore “infinite”, and assuming a tangentialrelationship of the acoustic wavefront to the beam path at some pointalong the beam path, the minimum detectable acoustic intensity in I_(a)in air is: $\begin{matrix}{I_{a} = \frac{h\quad c_{o}\lambda \quad B\quad \rho \quad c_{a}^{3}}{16\pi^{2}P_{o}\eta \quad \left( {n - 1} \right)^{2}R_{o}\Lambda}} & (2)\end{matrix}$

Substituting values into this equation, P_(o)=10 milliwatts, R_(o)=10,acoustic frequency=1 Khz, B=1 Khz, produces the 2.5×10⁻¹⁸ watt/cm²sensitivity noted earlier.

The differential acoustic pressure caused by the acoustic wave ofintensity Ia may be calculated by the relation— $\begin{matrix}{{\Delta \quad P_{a}} = \sqrt{I_{a}\rho \quad c_{a}}} & (3)\end{matrix}$

and the acoustic intensity of 2.5×10⁻¹⁸ watts/cm² corresponds to 3.25micropascals of rms pressure.

The minimum detectable acoustic power P_(a) emitted by the source thatcorresponds to this intensity can be found from the relation—$\begin{matrix}{I_{a} = \frac{P_{a}}{4\pi \quad R_{o}^{2}}} & (4)\end{matrix}$

Substituting this in the previous equation we have— $\begin{matrix}{P_{a} = \frac{\eta \quad c_{o}\lambda \quad B\quad \rho \quad c_{a}^{3}R_{o}}{4\pi \quad P_{o}{\eta \left( {n - 1} \right)}^{2}\Lambda}} & (5)\end{matrix}$

This shows that as the distance to the source, R_(o), decreases, theminimum power P_(a) decreases linearly with R_(o).

Another important situation to consider is the use of a reflector ofopportunity, which in general will be of a diffuse nature. Such asurface may be modeled by “Lambertian” behavior, in which the lightincident on the surface will be scattered into an entire hemisphere,with cosine angular weighting (cos θ in amplitude). As far as thebackscatter (reflection along illuminating axis) which is used fordetection is concerned, the behavior is equivalent to uniform scatteringinto π steradians. Thus the received scattering loss factor is defined:$\begin{matrix}{l_{scat} = \frac{P_{o}}{P_{T}}} & (6)\end{matrix}$

where P_(T) is the transmitted optical power. The scattering loss factorcan be expressed: $\begin{matrix}{l_{scat} = \frac{A_{R}r}{\pi \quad R_{o}^{2}}} & (7)\end{matrix}$

where A_(R) is the optical receiver aperture area, and r is thereflectivity of the scattering surface.

Using the previous example, with r=0.1, and a receiver aperture diameterof 5 cm: $\begin{matrix}{l_{scat} = {\frac{\frac{\pi}{4}({.05})^{2} \times 0.1}{\pi \quad \times 10^{2}} = {6.25 \times 10^{- 7}}}} & (8)\end{matrix}$

Incorporating this loss (P_(T)=10 milliwatts) into equation (2) producesa minimum detectable acoustic intensity of

3.95×10⁻¹² watts/cm²

and from equation (3) this corresponds to 4100 micro Pascals of rmspressure.

This is in the region of conversational speech levels (72 db re 1 uP).

Thus there is a dramatic loss associated with a diffuse target ascompared with a retro-reflector (mirror). However the resultingsensitivity can still provide useful detection with the quantum noiseassumption, and with favorable geometric relationships.

What is claimed is:
 1. A sensor for optically sensing air borne acousticwaves from a remote source, comprising: (a) means for producing mutuallycoherent optical sampling and reference beams, which may be combined toform a heterodyne or homodyne intermediate frequency carrier, saidsampling beam having a cross section which is small in relation to theacoustic wave lengths of interest, (b) optical means for defining a pathfor said sampling beam including an aperture through which the samplingbeam enters the air in which acoustic waves are borne, and through whichany light from said sampling beam passes after reflection, said aperturehaving a cross section which is small in relation to the acoustic wavelengths of interest, (c) light reflective means arranged in said pathfor reflecting significant sampling beam energy back via said aperture,said sampling beam path being oriented with a substantial componentparallel to the acoustic wavefronts of interest, so that the samplingbeam is exposed to an acoustic wave induced density variation of likeamplitude over a substantial portion of said path, said densityvariation producing a variation in the index of refraction, andthereupon phase modulation of the sampling beam in proportion to theaccumulated variation in the index of refraction over said beam path,(d) an optical detector including optical means for coherently combiningsaid reflected sampling beam with said reference beam to form anelectrical carrier, phase modulated as a result of said variation in theindex of refracton and (e) a phase detector coupled to the output ofsaid optical detector for detecting the acoustic wave induced phasevariation of said sampling beam and thereby recovering an electricalsignal representative of the acoustic waves.
 2. A sensor as set forth inclaim 1 wherein said light reflective means is a specular,retro-reflector, adjusted to reflect said beam back via said aperture.3. In combination, A. a plurality of sensors for optically sensing airborne acoustic waves along the boundaries of an area, each sensorcomprising: (a) means for producing mutually coherent, optical samplingand reference beams, which may be combined to form a heterodyne orhomodyne intermediate frequency carrier, (b) optical means for defininga path for said sampling beam including an aperture through which thesampling beam enters the air in which acoustic waves are borne, andthrough which any light from said sampling beam passes after reflection,said aperture having a cross section which is small in relation to theacoustic wave lengths of interest, (c) a specular, retro-reflectorarranged in said path for reflecting the sampling beam energy back viasaid aperture, each sampling beam path being oriented such that allacoustic sources along said beam path produce acoustic wavefrontstangential to said beam path, so that the sampling beam is exposed to anacoustic wave induced density variation of like amplitude over a portionof said path, said density variation producing a variation in the indexof refraction, and thereupon phase modulation of the sampling beam inproportion to the accumulated variation in the index of refraction oversaid beam path, (d) an optical detector including optical means forcoherently combining said reflected sampling beam with said referencebeam to form an electrical carrier, phase modulated as a result of saidvariation in the index of refracton, (e) a phase detector coupled to theoutput of said optical detector for detecting the acoustic wave inducedphase variation of said sampling beam and thereby producing anelectrical signal representative of the acoustic waves; and wherein B.each sensor is arranged so that the beam paths collectively form aclosed polygon embracing said area.